Thermodynamic and Topological Considerations

The thermodynamic stability of the fullerene-like materials is rather intricate and far from being fully understood. Such structures are not expected to be globally stable, but they are probably the stable phase of a layered compound, when the particles are not allowed to grow beyond, say a fraction of a micron. Therefore, there seems to exist a narrow window of conditions in the vicinity of the layered compound, itself, where nanophases of this kind exist. This idea is supported by a number of observations. For example, the W-S phase diagram provides a very convenient pathway for the synthesis of IF-WS2. The compound WS3, which is stable below 850°C under excess of sulfur, is amorphous. This compound will therefore lose sulfur atoms and crystallize into the compound WS2, which has a layered structure, upon heating or when sulfur is denied from its environment. If nanoparticles of WS3 are prepared and they are allowed to crystallize under the condition that no crystallite can grow beyond say 0.2|j.m, fullerene-like WS2 (MoS2) particles and nanotubes will become the favored phase. This principle serves as a principal guideline for the synthesis of bulk amounts of the IF-WS2 phase [40] and WS2 nanotubes in particular [8]. Unfortunately, in most cases, the situation is not as favorable, and more work is needed to clarify the existence zone of the IF phase in the phase diagram (in the vicinity of the layered compound).

Another very important implication of the formation of nanoparticles with IF structures is that in several cases it has been shown that the IF nanopar-ticles are stable, but the bulk form of the layered compound is either very difficult to synthesize or is totally unstable. The reason for this surprising observation is probably related to the fact that the IF structure is always closed and hence it does not expose reactive edges and interacts only very weakly with the ambient, which in many cases is hostile to the layered compound. For example, Na intercalated MoS2 is unstable in a moistured ambient, since water is sucked between the layers and into the van der Waals gap of the platelet and exfoliates it. In contrast, Na intercalated IF-MoS2 has been produced and was found to be stable in the ambient or even in suspensions [61]. Chalcogenides of the first row of transition metals, like CrSe2 and VS2, are not stable in the layered structure. However, Na intercalation endows extra stability to the layered structure, due to the charge transfer of electrons from the metal into the partially empty valence band of the host [62]. Thus, for example, NaCrSe2 and LiVS2 form a superlattice, in which the alkali metal layer and the transition metal layer alternate. The structure of this compound can be visualized akin to the layered structure CrSe2, in which the octahedral sites in the van der Waals gap between adajacent layers are fully occupied by the Na (Li) atoms. Nevertheless, VS2 nanoparticles with a fullerene-like structure, i.e., consisting of layered VS2, were found to be stable [61]. The unexpected extra stability of this structure emanates from the closed seamless structure of the IF, which does not expose the chemically reactive sites to the hostile environment. This idea opens new avenues for the synthesis of layered compounds, which could not be previously obtained or could not be exposed to the ambient [43], and therefore could only be studied to a limited extent.

Many layered compounds come in more than one stacking polytype [63]. For example, the two most abundant polytypes of MoS2 are the 2H and 3R. The 2H polytype is an abbreviation for the hexagonal structure consisting of two S-Mo-S layers in the unit cell (AbA- • BaB- • -AbA- • BaB, etc.). The 3R polytype has a rhombohedral unit cell of three repeating layers (AbA- - BcB- - -CaC- - -AbA- - BcB- - -CaC, etc.). In the case of MoS2, the most common polytype is the 2H form, but the 3R polytype was found, for example, in thin MoS2 films prepared by sputtering [64]. The nanotubes grown by the gas phase reaction between MoO3 and H2 S at 850° C were found to belong to the 2H polytype [4,65]. The same is true for WS2 nanotubes obtained from WO3 and H2S [8]. The appearance of the 3R polytype in such nanotubes can probably be associated with strain. For example, a "superlattice" of 2H and 3R polytypes was found to exist in MoS2 nanotubes grown by chemical vapor transport [22]. Strain effects are invoked to explain the preference of the rhombohedral polytype in both MoS2 and WS2 microtubes grown in the same way [21]. These observations indicate that the growth kinetics of the nanotubes and of thin films influence the strain relief mechanism, and therefore different polytypes can be adopted by the nanotubes.

The trigonal prismatic structure of MoS2 alludes to the possibility to form stable point defects consisting of a triangle or a rhombus [29]. In the past, evidence in support of the existence of "bucky-tetrahedra" [65] and "bucky-cubes" [66], which have four triangles and six rhombi in their corners, respectively, were found. However, the most compelling evidence in support of this idea was obtained in nanoparticles collected from the soot of laser ablated MoS2 [67]. Sharp cusps and even a rectangular apex were noticed in WS2 nanotubes, as well [8,9]. These features are probably a manifestation of the inherent stability of elements of symmetry lower than pentagons, such as triangles and rhombi, in the structure of MoS2, etc. They are preferentially formed by the cooling of the hot plasma soot of the ablated targets and are located in the nanotube apex or corners of the octahedra. Point defects of this symmetry were not observed in carbon fullerenes, most likely because the sp2 bonding of carbon atoms in graphite is not favorable for such topological elements. These examples and others illustrate the influence of the lattice structure of the layered compound on the detailed topology of the fullerene-like nanoparticle or of the nanotube cap obtained from such compounds.

The chemical composition of the IF phase deviates only very slightly, if at all, from the composition of the bulk layered compound. Deviations from stoichiometry can only occur in the cap of the nanotube. In fact, even the most modern analytical techniques, like scanning probe techniques and high (spatial) resolution electron energy loss spectroscopy are unable to resolve such a tiny change in the stoichiometry, like the excess or absence of a single Mo (W) or S (Se) atom in the nanotube cap.

The crystal structures of bulk graphite, BN, BC2N, and BC3 are quite similar to each other. They are all hexagonal layered structures, with ABAB packing being the most common arrangement of the layers. In the case of BC2N, two different sheet configurations are possible, leading to two different nanotube isomers with the same BC2N stoichiometry [68]. Figure 10 shows examples of such isomers with similar diameters.

Fig. 10. Theoretically determined tubules of isomers of BC2N. These are the (4,4) tubes, using the indexing protocol for carbon nanotubes. (courtesy of Y. Miyamoto [68])

4 Physical Properties

Early-on, a few groups used powerful theoretical tools to calculate the stability, band-structure and other physical properties of boron-nitride and boron carbo-nitride nanotubes [11,69,70,71]. A few striking conclusions emerged from these studies. First, it was found that B-B and N-N nearest neighbors do not lead to stable polyhedral structures. Instead, distinct B-N pairs of atoms were found to be thermodynamically preferred. This observation implies that B2N2 rectangles, rather than the 5-member rings found in carbon fullerenes and nanotubes, are required in order to stabilize the BN polyhe-dra and nanotubes. Experimental verification of this hypothesis has been obtained in the work of a few groups [51,72]. Secondly, in contrast to carbon nanotubes, which can be metallic or semiconducting depending on their chirality, all BN nanotubes were found to be semiconductors, independent of their chirality. Thirdly, whereas the smallest forbidden gap of the achiral (n, 0) nanotubes is a direct bandgap (r-r), an indirect bandgap (A-r) is calculated for the chiral nanotubes (n, m). Bulk BN material has an indirect bandgap of 5.8 eV. This is to be contrasted with carbon nanotubes, which are either metallic or semiconducting, depending on their (n, m) values (see Louie [73]). The fourth point to be noted is that, in contrast with carbon nanotubes in which the band gap increases with decreasing diameter, the bandgap of inorganic nanotubes was found to decrease with decreasing diameter of the IF nanotubes. This effect is attributed to the strain, and also to zone folding in the closed nanotube. The strain increases with decreasing diameter (D) of the nanotube as 1/D2. It should also be noted that generi-cally, the bandgap of semiconducting nanoparticles increases with decreasing particle diameter, which is attributed to the quantum size confinement of the electron wavefunction.

4.1 Band Structure Calculations

Figure 11 contrasts the band structures of BN in a sheet structure to that of BN in a nanotube structure. As mentioned above, BN nanotubes have a fairly robust bandgap, largely independent of the geometrical details of the nanotube. This uniformity suggests that BN nanotubes may present significant advantages over carbon nanotubes for specific applications. Details of the nanotube band structure show that the lowest lying conduction band state is a nearly free-electron like state which has a maximum charge density located about 0.2 nm interior to the tube wall. Thus, if BN tubes were injected with charge (say by modest doping), the resulting metallic tube would carry a cylinder of charge internally along its length.

Due to the greater complexity of BC2N, the unit cell of the bulk material is "double" that of graphite, and there are two possible arrangements of the B,C, and N atoms in the sheet, as reflected in the nanotubes of Fig. 10. The Type A sheet on the left (Fig. 10) has inversion symmetry (as does graphite) while the Type B sheet on the right (Fig. 10) does not (similar to BN). Consequently, the predicted electronic properties of Types A and B BC2N nano-tubes parallel the properties of carbon and BN nanotubes, respectively. Type

Fig. 11. Band structure of (a) BN sheet and (b) a BN (4,4) nanotube. (courtesy of S.G. Louie [17])

Fig. 11. Band structure of (a) BN sheet and (b) a BN (4,4) nanotube. (courtesy of S.G. Louie [17])

A BC2N nanotubes (Fig. 10a) range from semiconducting to metallic depending on diameter and chirality, while Type B BC2N nanotubes (Fig. 10b) are predicted to be semiconducting, independent of tube parameters. An interesting feature of Type B BC2N nanotubes is the arrangement of atoms in the tube wall fabric: a chain of potentially conducting carbon atoms alternating with a string of insulating BN. This resembles a solenoid, and doping a semiconducting Type B BC2N nanotube should result in a conducting tube where the electrical current spirals along the axis of the nanotube, forming a nano-coil.

The electrical behavior of BC3 is rather complex, but the most significant result from the theoretical calculations is that concentric tubes of BC3, or a close-packed array of mono-disperse single-walled BC3 tubes, are metallic, while isolated single-walled BC3 tubes are semiconducting [68].

Further work was carried out on nanotubes of the semiconducting layered compound GaSe [74]. In this compound, each atomic layer consists of a Ga-Ga dimer sandwiched between two outer selenium atoms in a hexagonal arrangement. This work indicated that some of the early observations made for BN and boro-carbonitride are not unique to these layered compounds, and are valid for a much wider group of structures. First, it was found that like the bulk material, GaSe nanotubes are semiconductors. Furthermore, the strain energy in the nanotube was shown to increase, and consequently the bandgap was found to shrink as the nanotube diameter becomes smaller. Recent work on WS2 and similar nanotubes [75] confirmed these earlier results. While the lowest bandgap of the armchair (n, n) nanotubes were found to be indirect, a direct transition was predicted for the zigzag (n, 0) nano-

tubes. Additionally, a similar dependence of the strain energy and bandgap energy on the nanotube diameter was predicted for WS2 nanotubes. These findings suggest a new mechanism for optical tuning through strain effects in the hollow nanocrystalline structures of layered compounds. The existence of a direct gap in zigzag nanotubes is rather important, since it suggests that such nanostructures may exhibit strong electroluminescence, which has never been observed for the bulk material.

The transport properties of inorganic nanotubes have not yet been reported. However, a wealth of information exists on the transport properties of the corresponding bulk quasi-2D materials, which is summarized in a few review articles [63,76].

4.2 Optical Studies in the UV and Visible

Measurements of the optical properties in this range of wavelengths can probe the fundamental electronic transitions in these nanostructures. Some of the aforementioned effects have in fact been experimentally revealed [77,78]. As mentioned above, the IF nanoparticles in this study were prepared by a careful sulfidization of oxide nanoparticles. Briefly, the reaction starts on the surface of the oxide nanoparticle and proceeds inwards, and hence the number of closed (fullerene-like) sulfide layers can be controlled quite accurately during the reaction. Also, the deeper the sulfide layer in the nanoparticle, the smaller is its radius and the larger is the strain in the nanostructure. Once available in sufficient quantities, the absorption spectra of thin films of the fullerene-like particles and nanotubes were measured at various temperatures (4-300 K). The excitonic nature of the absorption of the nanoparticles was established, which is a manifestation of the semiconductive nature of the material. Furthermore, a clear red shift in the exciton energy, which increased with the number of sulfide layers of the nanoparticles, was also observed (Fig. 12). The temperature dependence of the exciton energy was not very different from the behavior of the exciton in the bulk material. This observation indicates that the red shift in the exciton energy cannot be attributed to defects or dislocations in the IF material, but rather it is a genuine property of the inorganic fullerene-like and nanotube structures. In contrast to the previous observations, IF phases with less than 5 layers of sulfide revealed a clear blue shift in the excitonic transition energy, which was associated with the quantum size effect. Figure 13 summarizes this series of experiments and the two effects. The red shift of the exciton peak in the absorption measurements, due to strain in the bent layer on one hand, and the blue shift for the IF structures with very few layers and large diameter (minimum strain), on the other hand, can be discerned.

The WS2 and MoS2 nanotubes and the nested fullerene-like structures used for the experiments shown in Figs. 12 and 13 had relatively large diameters (>20 nm). Therefore, the strain energy is not particularly large in the first few closed layers of the sulfide, but the strain energy increases as

Fig. 12. Transmission electron microscopy (TEM) images and absorption spectra of crystalline and fullerene-like (IF) MoS2 films. (a) TEM micrograph of a partially converted nanoparticles with 5 layers of MoS2 and MoO2 core. (b) TEM micrograph of a fully converted IF-MoS2 nanoparticles. (c) Absorption spectra of various MoS2 particles. Curve-1 IF-MoS2 nanoparticles with MoO2 cores shown in (a); Curve-2 the fully converted (sulfidized) IF-MoS2 nanoparticles shown in (b). Curve-3 single crystal MoS2. Note the red shift of the excitonic peaks of the IF structure compared to those for the crystalline film. This shift increases as the number of closed MoS2 layers increases at the expense of the oxide core and their radii shrink [77]

Fig. 12. Transmission electron microscopy (TEM) images and absorption spectra of crystalline and fullerene-like (IF) MoS2 films. (a) TEM micrograph of a partially converted nanoparticles with 5 layers of MoS2 and MoO2 core. (b) TEM micrograph of a fully converted IF-MoS2 nanoparticles. (c) Absorption spectra of various MoS2 particles. Curve-1 IF-MoS2 nanoparticles with MoO2 cores shown in (a); Curve-2 the fully converted (sulfidized) IF-MoS2 nanoparticles shown in (b). Curve-3 single crystal MoS2. Note the red shift of the excitonic peaks of the IF structure compared to those for the crystalline film. This shift increases as the number of closed MoS2 layers increases at the expense of the oxide core and their radii shrink [77]

the oxide core is progressively converted into sulfide, i.e., closed sulfide layers of smaller and smaller diameter are formed. This unique experimental opportunity permitted a clear distinction to be made between the strain effect and the quantum size effect. In the early stages of the reaction, the strain is not very large and therefore the confinement of the exciton along the c-axis is evident from the blue shift in the exciton peak. The closed and therefore seamless nature of the MS2 layer is analogous to an infinite crystal in the a-b plane and hence quantum size effects in this plane can be ruled out. However, there is a clear confinement effect observable perpendicular to the a-b plane, i.e., in the c-direction. The quantum size effect in layered compounds was

Nanotubes from Inorganic Materials 103 1 00 i i i i | i i i i | i i i i | i i i i | i i i \m

Fig. 13. The dependence of the A exciton shifts on the number of layers in the IF structure. The x error bar represents the distribution of the number of layers determined with TEM for each sample. The y-axis error bar is ±10meV [77]

studied in the past [79,80]. The energy shift due to this effect (A Eg) can be expressed as:

h2 7T2h2

Here, ¡i\\ is the exciton effective mass parallel to the c-axis and Lz is the (average) thickness of the WSz nested structure (Lz = n x 0.62nm, where n is the number of WSz layers) in the nanoparticle. In a previous study of ultra-thin films of 2H-WSez, A Eg of the A exciton was found to obey (1) over a limited thickness range. A Eg was found to depend linearly on 1/L2z for Lz in the range of 4-7 nm and A Eg became asymptotically constant for Lz > 8nm [79]. A similar trend is observed for IF-WSz and MoSz, as shown in Fig. 14 [77]. Therefore, the quantum-size effect is indeed observed for IF structures with a very small number of WSz layers (n < 5). Note that in the current measurements, IF films 150 nm thick were used, but since each IF structure is isolated and the exciton cannot diffuse from one nanoparticle to another, the quantum size effect can be observed in this case. Note also, that due to the (residual) strain effect, the energy for both the A and B excitons is smaller than for their bulk counterparts. The corresponding red shift in the absorption spectrum has also been found for MoSz nanotubes [23].

These studies suggest a new kind of optical tuneability. Combined with the observation that zigzag inorganic nanotubes are predicted to exhibit direct optical transitions [75], new opportunities for optical device technology, e.g., MoSz nanotube based light-emitting diodes and lasers, could emerge from such studies in the future. The importance of strong light sources a few nm in size in future opto-electronic applications involving nanotechnology can be appreciated from the need to miniaturize current sub-micron light sources for lithography.

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